1. Technical Field
The present invention relates to a resonator element that vibrates in a flexural vibration mode, for example, and a resonator, an oscillator, and an electronic device each having the resonator element.
2. Related Art
In the related art, as a resonator element that vibrates in a flexural vibration mode, a tuning-fork type flexural resonator element has been widely used, for example. The flexural resonator element has a configuration in which a pair of resonating arms extends in parallel from a base portion of a base member made from a piezoelectric material such as quartz crystal so as to vibrate in a direction close to or away from each other in a horizontal direction.
If a vibration energy loss occurs when the resonating arms of the tuning-fork type flexural resonator element vibrate, the vibration energy loss can cause degradation of performance of the resonator element such as an increase in CI (crystal impedance) value and a decrease in the Q value. Therefore, various attempts have been made to prevent or reduce such a vibration energy loss.
For example, JP-A-2002-261575 and JP-A-2004-260718 disclose a tuning-fork type quartz crystal resonator element in which slits or slit-grooves having a predetermined depth are formed at both side portions of a base portion from which resonating arms extend. In the tuning-fork type quartz crystal resonator element, even when the vibration of the resonating arms includes a vertical component, vibration leak from the base portion is suppressed by the slits or the slit-grooves. Thus, a vibration energy trapping effect increases, and the Q value of the resonator element is controlled and variation of the Q values among resonator elements is prevented.
Moreover, in the resonator element, the vibration energy loss occurs due to not only such a mechanical cause as described above, but also other causes such as heat conduction caused by a temperature difference between a contracted portion, which receives compressive stress, and an expanded portion, which receives tensile stress, of each of the resonating arms which perform flexural vibration. The decrease in the Q value due to the heat conduction is called a thermoelastic loss effect.
In order to prevent or suppress the decrease in the Q value due to the thermoelastic loss effect (hereinafter simply referred to as a thermoelastic loss, for example, JP-UM-A-2-32229 proposes a tuning-fork type resonator element in which a groove or a hole is formed on the central line of a resonating arm (resonating beam) having a rectangular cross-section.
According to JP-UM-A-2-32229, based on a relational equation between distortion and stress which is well known in the case of internal friction of solids generally caused by temperature differences, the thermoelastic loss can be described that, when the frequency in a resonator element resonating in the flexural vibration mode changes, the Q value becomes minimum at a relaxation frequency fm=1/(2πτ) (here, τ is a relaxation time).
The relationship between the Q value and the frequency is generally expressed as a curve F in FIG. 11. In this figure, a frequency at which the Q value becomes minimum Q0 is a thermal relaxation frequency f0(=1/(2πτ)). That is, the thermal relaxation frequency f0 is the same as the relaxation frequency fm (for example, see C. Zener and two others, “Internal Friction in Solids, III. Experimental Demonstration of Thermoelastic Internal Friction,” PHYSICAL REVIEW, Volume 53, pp. 10-101 (Jan. 1, 1938)).
A tuning-fork type quartz crystal resonator element disclosed in JP-UM-A-2-32229 will be described in detail with reference to the drawings.
FIG. 10 is a plan view schematically showing a tuning-fork type quartz crystal resonator element as a typical example of a resonator element of the related art.
In FIG. 10, a tuning-fork type quartz crystal resonator element 1 of JP-UM-A-2-32229 includes two parallel resonating arms 3 and 4 extending from a base portion 2, and bottomed elongated grooves 6 and 7 having a straight-line shape are provided on the central line of each of the resonating arms 3 and 4. When a predetermined driving voltage is applied to excitation electrodes (not shown) of the tuning-fork type quartz crystal resonator element 1, the resonating arms 3 and 4 perform flexural vibration in a direction close to or away from each other as shown by imaginary lines (two-dot chain lines) and arrows in the figure.
By this flexural vibration, in the tuning-fork type quartz crystal resonator element 1, mechanical distortion occurs in a root portion of each of the resonating arms 3 and 4 attached to the base portion 2. That is, in the root portion of the resonating arm 3 attached to the base portion 2, a first region 10 which receives compressive or tensile stress due to the flexural vibration and a second region 11 which receives tensile stress when the first region 10 receives compressive stress while receiving compressive stress when the first region 10 receives tensile stress are present. The temperature of the first and second regions 10 and 11 increases when they receive compressive stress and decreases when they receive tensile stress.
Similarly, in the root portion of the resonating arm 4 attached to the base portion 2, a first region 12 which receives tensile or compressive stress due to the flexural vibration and a second region 13 which receives compressive stress when the first region 12 receives tensile stress while receiving tensile stress when the first region 12 receives compressive stress are present. The temperature of the first and second regions 12 and 13 increases when they receive compressive stress and decreases when they receive tensile stress.
By a temperature gradient taking place in this way, in the root portions of the resonating arms 3 and 4 attached to the base portion 2, heat conduction takes place between the first and second regions 10 and 11 and between the first and second regions 12 and 13. This temperature gradient takes place in a reverse direction so as to correspond to the flexural vibration of the resonating arms 3 and 4, and accordingly, the heat conduction also takes place in a reverse manner.
By this heat conduction, vibration energy of the resonating arms 3 and 4 is always partially lost as a thermoelastic loss during vibration. As a result, the Q value of the tuning-fork type quartz crystal resonator element 1 decreases and securing desired vibration properties is difficult.
In the tuning-fork type quartz crystal resonator element 1 of JP-UM-A-2-32229, since the transfer of heat from the contracted portion to the expanded portion is suppressed by the elongated grooves 6 and 7 provided on the central line of each of the resonating arms 3 and 4, it is possible to suppress or alleviate a decrease in the Q value due to a thermoelastic loss.
Meanwhile, in recent years, size-reduction techniques have been made in various products on which a vibration device having a resonator element is mounted, for example, small information apparatuses such as HDDs (hard disk drives), mobile computers, or IC cards, mobile communication apparatuses such as mobile phones, car-phones, or paging systems, and vibration gyro-sensors. With this trend, there is a further increasing demand for reducing the size of a vibration device (a resonator, an oscillator, and the like) mounted on these products and a resonator element accommodated in the vibration device.
For size-reduction of a resonator element, it is necessary to consider a problem in that mechanical strength will decrease if each part of the resonator element is made small or thin. Particularly, unless a predetermined level of rigidity is secured near a root portion of a resonating arm attached to a base portion where stress is concentrated when the resonator element vibrates, impact resistance against vibration stress and impact during dropping becomes insufficient. Thus, the resonator element may be destroyed.
As a resonator element which secures a predetermined level of such impact resistance, alleviates the mechanical or thermal vibration energy loss, and achieves size-reduction, for example, JP-A-2005-341251 discloses a resonator element in which the shape of an elongated groove formed in a resonating arm is innovated.
The resonator element (piezoelectric resonator element) disclosed in JP-A-2005-341251 includes a base portion made, for example, from quartz crystal, and a pair of resonating arms extending in parallel from the base portion. On the base portion, a pair of slits is formed in an opposing direction along one straight line so that a shrunken shape appears on both principal surfaces of the base portion.
Moreover, each resonating arm is provided with a bottomed elongated groove extending in a longitudinal direction of the resonating arm. The elongated groove is formed so that the groove width is small near a root portion of the resonating arm attached to the base portion and gradually increases as it goes towards the distal end of the resonating arm.
With this configuration, rigidity of the resonator element is strengthened in the elongated groove-formed regions of the root portions of the resonating arms attached to the base portion since the width of each bank portion formed between both side walls in the longitudinal direction of the elongated groove and both side surfaces of the resonating arm is larger as it goes towards the base portion rather than towards the distal end.
Accordingly, in the resonator element, it is possible to suppress the CI value with the elongated grooves and the slits while improving the impact resistance by strengthening the rigidity of the root portions of the resonating arms attached to the base portion. Moreover, it is possible to achieve size-reduction without degrading vibration properties while suppressing a decrease in the Q value.
However, in the resonator element disclosed in JP-A-2005-341251, since the elongated groove provided in the resonating arm has a shape such that the width gradually decreases from the distal end of the resonating arm to the base portion, the width of the bank portion formed in the longitudinal direction of the resonating arm increases near the root portion of the resonating arm attached to the base portion.
Due to this, in the resonator element, the thickness of a material serving as a heat conduction path for the transfer of heat from the contracted portion (high temperature portion) to the expanded portion (low temperature portion) during vibration of the resonating arm increases. Thus, a heat conduction time decreases and thermal relaxation is accelerated. Therefore, there is a problem in that the thermoelastic loss increases, the Q value decreases, and the vibration properties are degraded.